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arXiv · 2109.15178

Torus-like solutions for the Landau-de Gennes model. Part III: torus vs split minimizers

Federico Dipasquale·Vincent Millot·Adriano Pisante
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Abstract

We study the behaviour of global minimizers of a continuum Landau-de Gennes energy functional for nematic liquid crystals, in three-dimensional axially symmetric domains domains diffeomorphic to a ball (a nematic droplet) and in a restricted class of $\bbS^1$-equivariant configurations. It is known from our previous paper \cite{DMP2} that, assuming smooth and uniaxial (e.g. homeotropic) boundary conditions and a physically relevant norm constraint in the interior (Lyuksyutov constraint), minimizing configurations are either of \emph{torus} or of \emph{split} type. Here, starting from a nematic droplet with the homeotropic boundary condition, we show how singular (split) solutions or smooth (torus) solutions (or even both) for the Euler-Lagrange equations do appear as energy minimizers by suitably deforming either the domain or the boundary data. As a consequence, when minimizers among $\bbS^1$-equivariant configurations are singular we derive symmetry breaking result for the minimization among all competitors.

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Federico Dipasquale, Vincent Millot, Adriano Pisante. 2021-09-30. Torus-like solutions for the Landau-de Gennes model. Part III: torus vs split minimizers. https://arxiv.org/abs/2109.15178

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